A binary infinitesimal form of teichmüller metric and angles in an asymptotic teichmüller space

Yan Wu; Yi Qi

doi:10.1016/S0252-9602(16)30003-0

A binary infinitesimal form of teichmüller metric and angles in an asymptotic teichmüller space

Yan Wu
, Yi Qi

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The geometry of Teichmüller metric in an asymptotic Teichmüller space is studied in this article. First, a binary infinitesimal form of Teichmüller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmüller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.

Original language	English
Pages (from-to)	334-344
Number of pages	11
Journal	Acta Mathematica Scientia
Volume	36
Issue number	2
DOIs	https://doi.org/10.1016/S0252-9602(16)30003-0
State	Published - 1 Mar 2016

Keywords

Angles of asymptotic Teichmüller space
Boundary dilatation
Finsler structure
Geodesic segment

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10.1016/S0252-9602(16)30003-0

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title = "A binary infinitesimal form of teichm{\"u}ller metric and angles in an asymptotic teichm{\"u}ller space",

abstract = "The geometry of Teichm{\"u}ller metric in an asymptotic Teichm{\"u}ller space is studied in this article. First, a binary infinitesimal form of Teichm{\"u}ller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichm{\"u}ller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.",

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AU - Wu, Yan

AU - Qi, Yi

PY - 2016/3/1

Y1 - 2016/3/1

N2 - The geometry of Teichmüller metric in an asymptotic Teichmüller space is studied in this article. First, a binary infinitesimal form of Teichmüller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmüller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.

AB - The geometry of Teichmüller metric in an asymptotic Teichmüller space is studied in this article. First, a binary infinitesimal form of Teichmüller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmüller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.

KW - Angles of asymptotic Teichmüller space

KW - Boundary dilatation

KW - Finsler structure

KW - Geodesic segment

UR - https://www.scopus.com/pages/publications/84958165861

U2 - 10.1016/S0252-9602(16)30003-0

DO - 10.1016/S0252-9602(16)30003-0

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SN - 0252-9602

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JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 2

ER -

A binary infinitesimal form of teichmüller metric and angles in an asymptotic teichmüller space

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Keywords

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